Question

How do you use the graph to solve `0=x^2-8x+11`?

Answer 1

Look where the graph intersects the x axis.

graph{x^2-8x+11 [-10, 10, -5.21, 5.21]}

Explanation:

We can see that the graph of `x^2-8x+11=0` intersects the x axis at 2 distinct points, namely 1.764 and 6.236
So, the solutions of this equation are indeed those two values.

This happens because the graph is defined as `y=f(x)`. We want to find the values of x when y=0 (because it is known that y=0).
The graph intersects the x axis only when the y value is 0.
Therefore the solutions for the equation are the points where the graph intersects the x axis.